A 1997 Federal Highway Administration (FHWA) study found that raising or lowering speed limits by as much as 15 mph had very little effect on actual travel speeds. In many cases, raising a limit simply legalized the existing behavior of the majority without significantly increasing the top speeds.
Not sure if there has been a more recent study on this.
I’ll take my anecdotal evidence over this study. Whenever driving habits are discussed, people tend to report their speed relative to the speed limit. The idea of 7 or 9 mph over the limit keeps you from getting pulled over because of some rhyme has taken over in people’s minds. If the limit increases, so so the speed for most people I’ve talked to.
Now, there is certainly a limit to the point that people feel comfortable at a speed and may not go above that. So maybe raising it 15 mph hits that threshold. But I guarantee that people will get used to the higher speed eventually and then exceed it.